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Article Critique Morgan Coates Jenn Hartnett

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Overview Algebra concepts should be incorporated with elementary and middle school mathematics Math problems can be solved in multiple ways Everyone thinks different You can take a none algebraic problem and make it algebraic Manipulatives Even college students have trouble with algebra

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NCTM and NETS Standards NETS standards This article does inspire students to think of creative ways to solve math problems Using manipulatives There is really no mention of technology in this article NCTM website [grades 6-8] This article does “recognize and generate equivalent forms for simple algebraic expressions and solve linear equations” “develop an initial conceptual understanding of different uses of variables”

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Key Points Algebra can be easier to learn if it’s incorporated earlier in the learning process Using manipulatives is nothing but beneficial Hands on Visual Makes math problems more fun and practical You can take manipulatives and turn them into variables in an algebraic problem

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Example Using Manipulatives

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Example Using Variables

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Strengths Lots of specific examples Examples provide step by step reasoning and demonstration Explains reasoning as to why she is teaching her students the way she is Explains why the lesson is important for students Author explains in one part that she does not want to remind students what to do because she was “Interested in discovering what they would do when it was their turn to explore problems with manipulatives”. The use of a visual approach leading into using variables was a good transition. Ex: drawing a football, soccer ball, and baseball and later switching it to F, S, and B. Use classroom examples of college students, to show that we might need more work in trying to act like “elementary students”. Example: “It is interesting to note that a few students did solve the problems by using variables, even though I asked them not to. When I asked them why, they responded that they were so used to solving problems of this type by using variables that they could not solve them without using variables. The students’ struggles suggested to me that these preservice teachers need more practice with these strategies if they are expected to naturally implement them in their own classrooms.”

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Weaknesses When the author is describing her examples, for each step she states the fact first, followed by the explanation. When the author says “From fact 2, he finds the soccer ball’s weight,” it makes it a little difficult to follow along with. Spends a lot of time focusing on algebra, but when it comes to the elimination by subtraction part seems to go through it very fast. No technology mentioned

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How could technology be implemented into the classroom? All of the examples provided in the article could be displayed using a SmartBoard, or PowerPoint. Quizzes, Tests, Classroom activities, Homework could be implemented using technology The article does not show any implementation of technology.

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Assessment 1. When should algebra start to be incorporated? a. Highschool b. Middle School c. Elementary School d. College CORRECT ANSWER: C. Elementary School

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2. Which one of these statements is NOT a key point in the article? a. Algebra can be easier to learn if it’s incorporated earlier in the learning process b. Future teachers will never have to implement algebra into their lessons c. Using manipulatives is nothing but beneficial CORRECT ANSWER: B. Future teachers will never have to implement algebra into their lessons

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3. True or False: College students have no problem taking on the role of an elementary school student. CORRECT ANSWER: FALSE!!

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4. Which of these statements is true? a. There are good examples of technology applications in this article. b. The author spends an equal amount of time explaining substitution and subtraction. c. The author e xplains reasoning as to why she teaches her students the way she does. CORRECT ANSWER: c. The author explains reasoning as to why she teaches her students the way she does.

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5. True or False The author demonstrated a good explanation of the visual approach leading into the use of variables. CORRECT ANSWER: TRUE!!

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